The lines with postfix/smtpd show other people are trying to user your server as an smtp relay. Those connections are denied, which is a good thing.
The lines with postfix/smtp show that your outgoing email is not connecting to the smarthost where you want to deliver your email (I'm assuming). Try another smarthost which is allowed in your VPS environment.

That's what fail2ban does. It adds in rules to prevent attackers from accessing or abusing your system. You might get a lot of rules, but you will also notice your system will be much more responsive so you can work on other things.

Hackers and spammers search the web for open relays and try every trick in the book to attempt to get their message out to the real world. If you're system is seen as an open relay, then if an attacker is able to use your system for said relay, it would be you that gets blamed for allowing the message to be sent out, even if your system is deemed compromised.

Manage projects of all sizes how you want. Great for personal to-do lists, project milestones, team priorities and launch plans.
- Combine task lists, docs, spreadsheets, and chat in one
- View and edit from mobile/offline
- Cut down on emails

fail2ban is quite a good tool to start with if and only if you receive lots of connection attempts from the same ip. this should not be the case unless your server is the MX of a domain which you don't relay (or was recently)

if you configure it to ban an ip after the first relay access denied and possibly combine this with greylisting, you'll have something useful but it will quickly fill iptables with useless rules otherwise

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use postscreen so you can use postfix's builtin adaptive behavior

configure blacklists in postfix or use something like policydweight to protect further

then you can add spamassassin or the likes but the above steps should already block 90% of the spam traffic at least without even too much work on their config

@gheist : restrictions can be set in either files.
actually, i consider it best practice to enforce these restrictions in master when you have multiple smtpd services possibly linked with multiple cleanup services which is the case when you run content filters such as amavis(d-new)

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